We dedicate this paper to Prof. John B. Goodenough's 100th birthday, who has made several seminal contributions to the modern electrochemical energy storage and conversion technologies that made significant social and economic impacts on humankind. This review paper reports two battery systems that he contributed in the early stage of solid-state ionics (SSIs). The development of advanced Li and or Na batteries based on solid-state (ceramic) electrolytes (SSEs) is being focused on because of their safety, high energy density, and design flexibility for high power and energy density applications. Several SSEs exhibit a higher electrochemical stability window, enabling various high voltage cathodes to improve the power density compared to organic liquid electrolytes-based batteries (except for sulfide-based electrolytes). However, most SSEs have lower (at least an order of magnitude) ionic conductivity and poor interface compatibility compared to liquid electrolytes. Attempts have been made to improve the ionic conductivity and interface of SSEs and electrodes and develop hybrid solid electrolytes with improved ionic conductivity and stability with an elemental anode and high voltage cathodes. Here, we discuss the materials aspects of SSEs and hybrid SSEs for next-generation Li and Na batteries. Various solid-state electrolytes, including hydride-type, silicates, LISICONs, NASICON-type oxides, glassy-type oxides, covalent organic frameworks, perovskitetype oxides, antiperovskites, Li-stuffed garnet-related structure oxides, and metal halides have been developed. The chemical composition−structure−ionic conductivity relationship of several key SSEs and the ion transport mechanism have been discussed in this study. Moreover, interfacial engineering methods for some typical SSEs and battery applications have also been discussed.